Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,2,Mod(257,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([10, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.p (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.59326809096\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{12})\) |
Coefficient field: | 16.0.9349208943630483456.9 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 90) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 407.4 | ||
Root | \(0.500000 + 0.410882i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.407 |
Dual form | 450.2.p.h.293.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.258819 | + | 0.965926i | 0.183013 | + | 0.683013i | ||||
\(3\) | 0.0795432 | − | 1.73022i | 0.0459243 | − | 0.998945i | ||||
\(4\) | −0.866025 | + | 0.500000i | −0.433013 | + | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.69185 | − | 0.370982i | 0.690697 | − | 0.151453i | ||||
\(7\) | −3.75574 | + | 1.00635i | −1.41954 | + | 0.380364i | −0.885319 | − | 0.464984i | \(-0.846060\pi\) |
−0.534217 | + | 0.845347i | \(0.679394\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | −2.98735 | − | 0.275255i | −0.995782 | − | 0.0917517i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.44125 | − | 1.98681i | −1.03758 | − | 0.599044i | −0.118430 | − | 0.992962i | \(-0.537786\pi\) |
−0.919145 | + | 0.393918i | \(0.871119\pi\) | |||||||
\(12\) | 0.796225 | + | 1.53819i | 0.229850 | + | 0.444037i | ||||
\(13\) | −0.956351 | − | 0.256253i | −0.265244 | − | 0.0710719i | 0.123746 | − | 0.992314i | \(-0.460509\pi\) |
−0.388990 | + | 0.921242i | \(0.627176\pi\) | |||||||
\(14\) | −1.94411 | − | 3.36730i | −0.519586 | − | 0.899950i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | − | 0.866025i | 0.125000 | − | 0.216506i | ||||
\(17\) | 0.120239 | − | 0.120239i | 0.0291622 | − | 0.0291622i | −0.692375 | − | 0.721538i | \(-0.743436\pi\) |
0.721538 | + | 0.692375i | \(0.243436\pi\) | |||||||
\(18\) | −0.507306 | − | 2.95680i | −0.119573 | − | 0.696923i | ||||
\(19\) | − | 1.88492i | − | 0.432431i | −0.976346 | − | 0.216216i | \(-0.930629\pi\) | ||
0.976346 | − | 0.216216i | \(-0.0693714\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.44246 | + | 6.57832i | 0.314771 | + | 1.43551i | ||||
\(22\) | 1.02845 | − | 3.83821i | 0.219265 | − | 0.818310i | ||||
\(23\) | −1.36362 | + | 5.08911i | −0.284335 | + | 1.06115i | 0.664989 | + | 0.746853i | \(0.268436\pi\) |
−0.949324 | + | 0.314299i | \(0.898230\pi\) | |||||||
\(24\) | −1.27970 | + | 1.16721i | −0.261217 | + | 0.238255i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 0.990087i | − | 0.194172i | ||||||
\(27\) | −0.713876 | + | 5.14688i | −0.137386 | + | 0.990518i | ||||
\(28\) | 2.74939 | − | 2.74939i | 0.519586 | − | 0.519586i | ||||
\(29\) | −2.15618 | + | 3.73461i | −0.400392 | + | 0.693499i | −0.993773 | − | 0.111422i | \(-0.964459\pi\) |
0.593381 | + | 0.804922i | \(0.297793\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.70172 | − | 8.14362i | −0.844454 | − | 1.46264i | −0.886095 | − | 0.463504i | \(-0.846592\pi\) |
0.0416413 | − | 0.999133i | \(-0.486741\pi\) | |||||||
\(32\) | 0.965926 | + | 0.258819i | 0.170753 | + | 0.0457532i | ||||
\(33\) | −3.71134 | + | 5.79609i | −0.646062 | + | 1.00897i | ||||
\(34\) | 0.147262 | + | 0.0850217i | 0.0252552 | + | 0.0145811i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.72474 | − | 1.25529i | 0.454124 | − | 0.209216i | ||||
\(37\) | −3.26863 | − | 3.26863i | −0.537360 | − | 0.537360i | 0.385393 | − | 0.922753i | \(-0.374066\pi\) |
−0.922753 | + | 0.385393i | \(0.874066\pi\) | |||||||
\(38\) | 1.82070 | − | 0.487854i | 0.295356 | − | 0.0791404i | ||||
\(39\) | −0.519447 | + | 1.63432i | −0.0831781 | + | 0.261700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.15775 | − | 4.13253i | 1.11785 | − | 0.645393i | 0.177001 | − | 0.984211i | \(-0.443360\pi\) |
0.940852 | + | 0.338818i | \(0.110027\pi\) | |||||||
\(42\) | −5.98083 | + | 3.09591i | −0.922862 | + | 0.477709i | ||||
\(43\) | −0.533983 | − | 1.99285i | −0.0814316 | − | 0.303907i | 0.913183 | − | 0.407550i | \(-0.133617\pi\) |
−0.994615 | + | 0.103643i | \(0.966950\pi\) | |||||||
\(44\) | 3.97361 | 0.599044 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.26863 | −0.776818 | ||||||||
\(47\) | −0.897060 | − | 3.34787i | −0.130850 | − | 0.488338i | 0.869131 | − | 0.494582i | \(-0.164679\pi\) |
−0.999981 | + | 0.00624459i | \(0.998012\pi\) | |||||||
\(48\) | −1.45865 | − | 0.933998i | −0.210537 | − | 0.134811i | ||||
\(49\) | 7.03067 | − | 4.05916i | 1.00438 | − | 0.579880i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.198476 | − | 0.217604i | −0.0277922 | − | 0.0304707i | ||||
\(52\) | 0.956351 | − | 0.256253i | 0.132622 | − | 0.0355359i | ||||
\(53\) | 3.66571 | + | 3.66571i | 0.503524 | + | 0.503524i | 0.912531 | − | 0.409007i | \(-0.134125\pi\) |
−0.409007 | + | 0.912531i | \(0.634125\pi\) | |||||||
\(54\) | −5.15627 | + | 0.642559i | −0.701679 | + | 0.0874413i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.36730 | + | 1.94411i | 0.449975 | + | 0.259793i | ||||
\(57\) | −3.26134 | − | 0.149933i | −0.431975 | − | 0.0198591i | ||||
\(58\) | −4.16541 | − | 1.11612i | −0.546946 | − | 0.146554i | ||||
\(59\) | 2.72877 | + | 4.72637i | 0.355255 | + | 0.615320i | 0.987162 | − | 0.159724i | \(-0.0510606\pi\) |
−0.631906 | + | 0.775045i | \(0.717727\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.35623 | + | 7.54520i | −0.557758 | + | 0.966064i | 0.439926 | + | 0.898034i | \(0.355005\pi\) |
−0.997683 | + | 0.0680302i | \(0.978329\pi\) | |||||||
\(62\) | 6.64923 | − | 6.64923i | 0.844454 | − | 0.844454i | ||||
\(63\) | 11.4967 | − | 1.97252i | 1.44845 | − | 0.248514i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.55916 | − | 2.08475i | −0.807377 | − | 0.256614i | ||||
\(67\) | 2.10759 | − | 7.86563i | 0.257483 | − | 0.960940i | −0.709209 | − | 0.704998i | \(-0.750948\pi\) |
0.966692 | − | 0.255942i | \(-0.0823855\pi\) | |||||||
\(68\) | −0.0440105 | + | 0.164249i | −0.00533705 | + | 0.0199182i | ||||
\(69\) | 8.69683 | + | 2.76418i | 1.04698 | + | 0.332768i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.94911i | 0.824708i | 0.911024 | + | 0.412354i | \(0.135293\pi\) | ||||
−0.911024 | + | 0.412354i | \(0.864707\pi\) | |||||||
\(72\) | 1.91774 | + | 2.30701i | 0.226008 | + | 0.271883i | ||||
\(73\) | 8.27728 | − | 8.27728i | 0.968783 | − | 0.968783i | −0.0307446 | − | 0.999527i | \(-0.509788\pi\) |
0.999527 | + | 0.0307446i | \(0.00978785\pi\) | |||||||
\(74\) | 2.31127 | − | 4.00324i | 0.268680 | − | 0.465368i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.942462 | + | 1.63239i | 0.108108 | + | 0.187248i | ||||
\(77\) | 14.9238 | + | 3.99883i | 1.70073 | + | 0.455709i | ||||
\(78\) | −1.71307 | − | 0.0787547i | −0.193967 | − | 0.00891722i | ||||
\(79\) | −11.7529 | − | 6.78553i | −1.32230 | − | 0.763431i | −0.338206 | − | 0.941072i | \(-0.609820\pi\) |
−0.984095 | + | 0.177641i | \(0.943153\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.84847 | + | 1.64456i | 0.983163 | + | 0.182729i | ||||
\(82\) | 5.84428 | + | 5.84428i | 0.645393 | + | 0.645393i | ||||
\(83\) | −6.75913 | + | 1.81110i | −0.741911 | + | 0.198795i | −0.609927 | − | 0.792457i | \(-0.708801\pi\) |
−0.131984 | + | 0.991252i | \(0.542135\pi\) | |||||||
\(84\) | −4.53837 | − | 4.97576i | −0.495176 | − | 0.542900i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.78674 | − | 1.03157i | 0.192669 | − | 0.111238i | ||||
\(87\) | 6.29020 | + | 4.02773i | 0.674380 | + | 0.431818i | ||||
\(88\) | 1.02845 | + | 3.83821i | 0.109633 | + | 0.409155i | ||||
\(89\) | 4.87832 | 0.517100 | 0.258550 | − | 0.965998i | \(-0.416755\pi\) | ||||
0.258550 | + | 0.965998i | \(0.416755\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.84968 | 0.403557 | ||||||||
\(92\) | −1.36362 | − | 5.08911i | −0.142168 | − | 0.530576i | ||||
\(93\) | −14.4643 | + | 7.48725i | −1.49987 | + | 0.776392i | ||||
\(94\) | 3.00162 | − | 1.73299i | 0.309594 | − | 0.178744i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.524648 | − | 1.65068i | 0.0535466 | − | 0.168472i | ||||
\(97\) | −1.44518 | + | 0.387234i | −0.146736 | + | 0.0393177i | −0.331439 | − | 0.943477i | \(-0.607534\pi\) |
0.184704 | + | 0.982794i | \(0.440868\pi\) | |||||||
\(98\) | 5.74052 | + | 5.74052i | 0.579880 | + | 0.579880i | ||||
\(99\) | 9.73332 | + | 6.88249i | 0.978235 | + | 0.691717i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.91944 | − | 5.14964i | −0.887517 | − | 0.512408i | −0.0143875 | − | 0.999896i | \(-0.504580\pi\) |
−0.873130 | + | 0.487488i | \(0.837913\pi\) | |||||||
\(102\) | 0.158820 | − | 0.248033i | 0.0157255 | − | 0.0245589i | ||||
\(103\) | 6.26326 | + | 1.67823i | 0.617137 | + | 0.165361i | 0.553826 | − | 0.832632i | \(-0.313167\pi\) |
0.0633111 | + | 0.997994i | \(0.479834\pi\) | |||||||
\(104\) | 0.495044 | + | 0.857441i | 0.0485430 | + | 0.0840790i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.59205 | + | 4.48956i | −0.251762 | + | 0.436065i | ||||
\(107\) | −3.70057 | + | 3.70057i | −0.357747 | + | 0.357747i | −0.862982 | − | 0.505235i | \(-0.831406\pi\) |
0.505235 | + | 0.862982i | \(0.331406\pi\) | |||||||
\(108\) | −1.95521 | − | 4.81427i | −0.188140 | − | 0.463253i | ||||
\(109\) | 7.30160i | 0.699367i | 0.936868 | + | 0.349683i | \(0.113711\pi\) | ||||
−0.936868 | + | 0.349683i | \(0.886289\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.91546 | + | 5.39547i | −0.561471 | + | 0.512115i | ||||
\(112\) | −1.00635 | + | 3.75574i | −0.0950909 | + | 0.354884i | ||||
\(113\) | 1.09205 | − | 4.07557i | 0.102731 | − | 0.383397i | −0.895347 | − | 0.445369i | \(-0.853072\pi\) |
0.998078 | + | 0.0619722i | \(0.0197390\pi\) | |||||||
\(114\) | −0.699273 | − | 3.18902i | −0.0654929 | − | 0.298679i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 4.31235i | − | 0.400392i | ||||||
\(117\) | 2.78641 | + | 1.02876i | 0.257604 | + | 0.0951087i | ||||
\(118\) | −3.85906 | + | 3.85906i | −0.355255 | + | 0.355255i | ||||
\(119\) | −0.330584 | + | 0.572588i | −0.0303046 | + | 0.0524891i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.39479 | + | 4.14790i | 0.217708 | + | 0.377081i | ||||
\(122\) | −8.41558 | − | 2.25495i | −0.761911 | − | 0.204153i | ||||
\(123\) | −6.58085 | − | 12.7132i | −0.593375 | − | 1.14631i | ||||
\(124\) | 8.14362 | + | 4.70172i | 0.731318 | + | 0.422227i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.88087 | + | 10.5944i | 0.434823 | + | 0.943827i | ||||
\(127\) | −13.7871 | − | 13.7871i | −1.22341 | − | 1.22341i | −0.966411 | − | 0.257000i | \(-0.917266\pi\) |
−0.257000 | − | 0.966411i | \(-0.582734\pi\) | |||||||
\(128\) | −0.965926 | + | 0.258819i | −0.0853766 | + | 0.0228766i | ||||
\(129\) | −3.49055 | + | 0.765391i | −0.307326 | + | 0.0673889i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.88249 | + | 2.24156i | −0.339215 | + | 0.195846i | −0.659925 | − | 0.751332i | \(-0.729412\pi\) |
0.320710 | + | 0.947178i | \(0.396079\pi\) | |||||||
\(132\) | 0.316074 | − | 6.87523i | 0.0275107 | − | 0.598412i | ||||
\(133\) | 1.89689 | + | 7.07929i | 0.164481 | + | 0.613852i | ||||
\(134\) | 8.14310 | 0.703457 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.170043 | −0.0145811 | ||||||||
\(137\) | 3.23492 | + | 12.0729i | 0.276378 | + | 1.03146i | 0.954912 | + | 0.296888i | \(0.0959489\pi\) |
−0.678534 | + | 0.734569i | \(0.737384\pi\) | |||||||
\(138\) | −0.419084 | + | 9.11591i | −0.0356748 | + | 0.775998i | ||||
\(139\) | 3.60435 | − | 2.08097i | 0.305717 | − | 0.176506i | −0.339291 | − | 0.940681i | \(-0.610187\pi\) |
0.645008 | + | 0.764176i | \(0.276854\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.86393 | + | 1.28581i | −0.493832 | + | 0.108285i | ||||
\(142\) | −6.71233 | + | 1.79856i | −0.563286 | + | 0.150932i | ||||
\(143\) | 2.78191 | + | 2.78191i | 0.232635 | + | 0.232635i | ||||
\(144\) | −1.73205 | + | 2.44949i | −0.144338 | + | 0.204124i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 10.1376 | + | 5.85292i | 0.838990 | + | 0.484391i | ||||
\(147\) | −6.46401 | − | 12.4875i | −0.533143 | − | 1.02995i | ||||
\(148\) | 4.46504 | + | 1.19640i | 0.367024 | + | 0.0983437i | ||||
\(149\) | 0.518244 | + | 0.897625i | 0.0424562 | + | 0.0735363i | 0.886473 | − | 0.462781i | \(-0.153148\pi\) |
−0.844016 | + | 0.536317i | \(0.819815\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.03451 | + | 3.52388i | −0.165566 | + | 0.286769i | −0.936856 | − | 0.349715i | \(-0.886278\pi\) |
0.771290 | + | 0.636484i | \(0.219612\pi\) | |||||||
\(152\) | −1.33284 | + | 1.33284i | −0.108108 | + | 0.108108i | ||||
\(153\) | −0.392291 | + | 0.326099i | −0.0317149 | + | 0.0263635i | ||||
\(154\) | 15.4503i | 1.24502i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.367304 | − | 1.67508i | −0.0294079 | − | 0.134114i | ||||
\(157\) | −2.36186 | + | 8.81460i | −0.188497 | + | 0.703481i | 0.805357 | + | 0.592789i | \(0.201973\pi\) |
−0.993855 | + | 0.110692i | \(0.964693\pi\) | |||||||
\(158\) | 3.51245 | − | 13.1086i | 0.279435 | − | 1.04287i | ||||
\(159\) | 6.63408 | − | 6.05092i | 0.526117 | − | 0.479869i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 20.4857i | − | 1.61450i | ||||||
\(162\) | 0.701625 | + | 8.97261i | 0.0551249 | + | 0.704955i | ||||
\(163\) | −5.03848 | + | 5.03848i | −0.394644 | + | 0.394644i | −0.876339 | − | 0.481695i | \(-0.840021\pi\) |
0.481695 | + | 0.876339i | \(0.340021\pi\) | |||||||
\(164\) | −4.13253 | + | 7.15775i | −0.322696 | + | 0.558926i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.49878 | − | 6.06007i | −0.271558 | − | 0.470353i | ||||
\(167\) | 10.4641 | + | 2.80384i | 0.809734 | + | 0.216968i | 0.639853 | − | 0.768497i | \(-0.278995\pi\) |
0.169881 | + | 0.985465i | \(0.445662\pi\) | |||||||
\(168\) | 3.63160 | − | 5.67155i | 0.280184 | − | 0.437569i | ||||
\(169\) | −10.4094 | − | 6.00986i | −0.800722 | − | 0.462297i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.518835 | + | 5.63092i | −0.0396763 | + | 0.430607i | ||||
\(172\) | 1.45887 | + | 1.45887i | 0.111238 | + | 0.111238i | ||||
\(173\) | −3.64139 | + | 0.975709i | −0.276850 | + | 0.0741818i | −0.394573 | − | 0.918865i | \(-0.629107\pi\) |
0.117722 | + | 0.993047i | \(0.462441\pi\) | |||||||
\(174\) | −2.26247 | + | 7.11832i | −0.171517 | + | 0.539638i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.44125 | + | 1.98681i | −0.259394 | + | 0.149761i | ||||
\(177\) | 8.39472 | − | 4.34543i | 0.630986 | − | 0.326622i | ||||
\(178\) | 1.26260 | + | 4.71209i | 0.0946359 | + | 0.353186i | ||||
\(179\) | −12.8952 | −0.963836 | −0.481918 | − | 0.876216i | \(-0.660060\pi\) | ||||
−0.481918 | + | 0.876216i | \(0.660060\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.3197 | 1.80767 | 0.903835 | − | 0.427881i | \(-0.140740\pi\) | ||||
0.903835 | + | 0.427881i | \(0.140740\pi\) | |||||||
\(182\) | 0.996372 | + | 3.71851i | 0.0738560 | + | 0.275634i | ||||
\(183\) | 12.7084 | + | 8.13741i | 0.939430 | + | 0.601535i | ||||
\(184\) | 4.56277 | − | 2.63432i | 0.336372 | − | 0.194204i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −10.9758 | − | 12.0336i | −0.804782 | − | 0.882344i | ||||
\(187\) | −0.652663 | + | 0.174880i | −0.0477274 | + | 0.0127885i | ||||
\(188\) | 2.45081 | + | 2.45081i | 0.178744 | + | 0.178744i | ||||
\(189\) | −2.49842 | − | 20.0488i | −0.181733 | − | 1.45833i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.8036 | + | 6.81478i | 0.854075 | + | 0.493100i | 0.862024 | − | 0.506868i | \(-0.169197\pi\) |
−0.00794868 | + | 0.999968i | \(0.502530\pi\) | |||||||
\(192\) | 1.73022 | + | 0.0795432i | 0.124868 | + | 0.00574054i | ||||
\(193\) | −15.6521 | − | 4.19397i | −1.12666 | − | 0.301889i | −0.353086 | − | 0.935591i | \(-0.614868\pi\) |
−0.773577 | + | 0.633702i | \(0.781534\pi\) | |||||||
\(194\) | −0.748079 | − | 1.29571i | −0.0537090 | − | 0.0930267i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.05916 | + | 7.03067i | −0.289940 | + | 0.502191i | ||||
\(197\) | −1.16085 | + | 1.16085i | −0.0827072 | + | 0.0827072i | −0.747250 | − | 0.664543i | \(-0.768626\pi\) |
0.664543 | + | 0.747250i | \(0.268626\pi\) | |||||||
\(198\) | −4.12881 | + | 11.1830i | −0.293422 | + | 0.794740i | ||||
\(199\) | − | 17.1733i | − | 1.21738i | −0.793407 | − | 0.608691i | \(-0.791695\pi\) | ||
0.793407 | − | 0.608691i | \(-0.208305\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.4417 | − | 4.27226i | −0.948101 | − | 0.301342i | ||||
\(202\) | 2.66565 | − | 9.94834i | 0.187554 | − | 0.699963i | ||||
\(203\) | 4.33973 | − | 16.1961i | 0.304589 | − | 1.13674i | ||||
\(204\) | 0.280687 | + | 0.0892129i | 0.0196520 | + | 0.00624615i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.48420i | 0.451776i | ||||||||
\(207\) | 5.47442 | − | 14.8276i | 0.380498 | − | 1.03059i | ||||
\(208\) | −0.700097 | + | 0.700097i | −0.0485430 | + | 0.0485430i | ||||
\(209\) | −3.74498 | + | 6.48649i | −0.259046 | + | 0.448680i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.10894 | − | 15.7771i | −0.627085 | − | 1.08614i | −0.988134 | − | 0.153597i | \(-0.950914\pi\) |
0.361048 | − | 0.932547i | \(-0.382419\pi\) | |||||||
\(212\) | −5.00745 | − | 1.34174i | −0.343913 | − | 0.0921513i | ||||
\(213\) | 12.0235 | + | 0.552755i | 0.823838 | + | 0.0378741i | ||||
\(214\) | −4.53225 | − | 2.61670i | −0.309818 | − | 0.178874i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.14418 | − | 3.13461i | 0.281976 | − | 0.213283i | ||||
\(217\) | 25.8537 | + | 25.8537i | 1.75507 | + | 1.75507i | ||||
\(218\) | −7.05281 | + | 1.88979i | −0.477676 | + | 0.127993i | ||||
\(219\) | −13.6631 | − | 14.9799i | −0.923270 | − | 1.01225i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.145802 | + | 0.0841789i | −0.00980771 | + | 0.00566249i | ||||
\(222\) | −6.74266 | − | 4.31745i | −0.452538 | − | 0.289768i | ||||
\(223\) | −1.21534 | − | 4.53570i | −0.0813849 | − | 0.303733i | 0.913220 | − | 0.407466i | \(-0.133588\pi\) |
−0.994605 | + | 0.103734i | \(0.966921\pi\) | |||||||
\(224\) | −3.88823 | −0.259793 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.21934 | 0.280666 | ||||||||
\(227\) | −6.47859 | − | 24.1784i | −0.429999 | − | 1.60478i | −0.752758 | − | 0.658297i | \(-0.771277\pi\) |
0.322759 | − | 0.946481i | \(-0.395390\pi\) | |||||||
\(228\) | 2.89937 | − | 1.50082i | 0.192015 | − | 0.0993945i | ||||
\(229\) | −19.7350 | + | 11.3940i | −1.30412 | + | 0.752935i | −0.981108 | − | 0.193459i | \(-0.938029\pi\) |
−0.323014 | + | 0.946394i | \(0.604696\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.10596 | − | 25.5035i | 0.533333 | − | 1.67801i | ||||
\(232\) | 4.16541 | − | 1.11612i | 0.273473 | − | 0.0732768i | ||||
\(233\) | −20.6491 | − | 20.6491i | −1.35277 | − | 1.35277i | −0.882553 | − | 0.470214i | \(-0.844177\pi\) |
−0.470214 | − | 0.882553i | \(-0.655823\pi\) | |||||||
\(234\) | −0.272527 | + | 2.95773i | −0.0178156 | + | 0.193353i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.72637 | − | 2.72877i | −0.307660 | − | 0.177628i | ||||
\(237\) | −12.6753 | + | 19.7954i | −0.823352 | + | 1.28585i | ||||
\(238\) | −0.638639 | − | 0.171123i | −0.0413968 | − | 0.0110922i | ||||
\(239\) | −4.56277 | − | 7.90295i | −0.295141 | − | 0.511199i | 0.679877 | − | 0.733327i | \(-0.262033\pi\) |
−0.975018 | + | 0.222127i | \(0.928700\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.869654 | − | 1.50629i | 0.0560194 | − | 0.0970284i | −0.836656 | − | 0.547729i | \(-0.815492\pi\) |
0.892675 | + | 0.450701i | \(0.148826\pi\) | |||||||
\(242\) | −3.38674 | + | 3.38674i | −0.217708 | + | 0.217708i | ||||
\(243\) | 3.54930 | − | 15.1790i | 0.227688 | − | 0.973734i | ||||
\(244\) | − | 8.71245i | − | 0.557758i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 10.5768 | − | 9.64703i | 0.674351 | − | 0.615072i | ||||
\(247\) | −0.483018 | + | 1.80265i | −0.0307337 | + | 0.114700i | ||||
\(248\) | −2.43379 | + | 9.08302i | −0.154546 | + | 0.576773i | ||||
\(249\) | 2.59597 | + | 11.8389i | 0.164513 | + | 0.750258i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.16751i | 0.389290i | 0.980874 | + | 0.194645i | \(0.0623555\pi\) | ||||
−0.980874 | + | 0.194645i | \(0.937645\pi\) | |||||||
\(252\) | −8.97017 | + | 7.45660i | −0.565068 | + | 0.469722i | ||||
\(253\) | 14.8036 | − | 14.8036i | 0.930696 | − | 0.930696i | ||||
\(254\) | 9.74898 | − | 16.8857i | 0.611706 | − | 1.05951i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −28.0634 | − | 7.51956i | −1.75055 | − | 0.469057i | −0.765803 | − | 0.643075i | \(-0.777658\pi\) |
−0.984743 | + | 0.174018i | \(0.944325\pi\) | |||||||
\(258\) | −1.64273 | − | 3.17351i | −0.102272 | − | 0.197574i | ||||
\(259\) | 15.5655 | + | 8.98676i | 0.967194 | + | 0.558410i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.46922 | − | 10.5631i | 0.462333 | − | 0.653838i | ||||
\(262\) | −3.17004 | − | 3.17004i | −0.195846 | − | 0.195846i | ||||
\(263\) | 18.0249 | − | 4.82975i | 1.11146 | − | 0.297815i | 0.344038 | − | 0.938956i | \(-0.388205\pi\) |
0.767424 | + | 0.641141i | \(0.221538\pi\) | |||||||
\(264\) | 6.72277 | − | 1.47414i | 0.413758 | − | 0.0907269i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −6.34711 | + | 3.66451i | −0.389167 | + | 0.224685i | ||||
\(267\) | 0.388037 | − | 8.44057i | 0.0237475 | − | 0.516555i | ||||
\(268\) | 2.10759 | + | 7.86563i | 0.128742 | + | 0.480470i | ||||
\(269\) | −15.5553 | −0.948425 | −0.474212 | − | 0.880411i | \(-0.657267\pi\) | ||||
−0.474212 | + | 0.880411i | \(0.657267\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.87184 | −0.113706 | −0.0568532 | − | 0.998383i | \(-0.518107\pi\) | ||||
−0.0568532 | + | 0.998383i | \(0.518107\pi\) | |||||||
\(272\) | −0.0440105 | − | 0.164249i | −0.00266853 | − | 0.00995908i | ||||
\(273\) | 0.306216 | − | 6.66081i | 0.0185331 | − | 0.403131i | ||||
\(274\) | −10.8243 | + | 6.24939i | −0.653918 | + | 0.377540i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −8.91376 | + | 1.95457i | −0.536545 | + | 0.117651i | ||||
\(277\) | −3.99035 | + | 1.06921i | −0.239757 | + | 0.0642426i | −0.376696 | − | 0.926337i | \(-0.622940\pi\) |
0.136940 | + | 0.990579i | \(0.456273\pi\) | |||||||
\(278\) | 2.94294 | + | 2.94294i | 0.176506 | + | 0.176506i | ||||
\(279\) | 11.8041 | + | 25.6220i | 0.706692 | + | 1.53395i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.248640 | + | 0.143552i | 0.0148326 | + | 0.00856361i | 0.507398 | − | 0.861712i | \(-0.330607\pi\) |
−0.492565 | + | 0.870275i | \(0.663941\pi\) | |||||||
\(282\) | −2.75970 | − | 5.33132i | −0.164338 | − | 0.317476i | ||||
\(283\) | −17.4857 | − | 4.68527i | −1.03941 | − | 0.278510i | −0.301544 | − | 0.953452i | \(-0.597502\pi\) |
−0.737871 | + | 0.674942i | \(0.764169\pi\) | |||||||
\(284\) | −3.47456 | − | 6.01811i | −0.206177 | − | 0.357109i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.96711 | + | 3.40713i | −0.116318 | + | 0.201468i | ||||
\(287\) | −22.7239 | + | 22.7239i | −1.34135 | + | 1.34135i | ||||
\(288\) | −2.81431 | − | 1.03906i | −0.165835 | − | 0.0612271i | ||||
\(289\) | 16.9711i | 0.998299i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.555048 | + | 2.53128i | 0.0325375 | + | 0.148386i | ||||
\(292\) | −3.02970 | + | 11.3070i | −0.177300 | + | 0.661691i | ||||
\(293\) | −5.53752 | + | 20.6663i | −0.323505 | + | 1.20734i | 0.592300 | + | 0.805717i | \(0.298220\pi\) |
−0.915806 | + | 0.401621i | \(0.868447\pi\) | |||||||
\(294\) | 10.3890 | − | 9.47576i | 0.605899 | − | 0.552637i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.62255i | 0.268680i | ||||||||
\(297\) | 12.6825 | − | 16.2934i | 0.735912 | − | 0.945436i | ||||
\(298\) | −0.732907 | + | 0.732907i | −0.0424562 | + | 0.0424562i | ||||
\(299\) | 2.60820 | − | 4.51754i | 0.150836 | − | 0.261256i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.01100 | + | 6.94725i | 0.231190 | + | 0.400433i | ||||
\(302\) | −3.93037 | − | 1.05314i | −0.226168 | − | 0.0606014i | ||||
\(303\) | −9.61951 | + | 15.0230i | −0.552626 | + | 0.863049i | ||||
\(304\) | −1.63239 | − | 0.942462i | −0.0936241 | − | 0.0540539i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.416520 | − | 0.294524i | −0.0238108 | − | 0.0168368i | ||||
\(307\) | 20.2953 | + | 20.2953i | 1.15831 | + | 1.15831i | 0.984838 | + | 0.173476i | \(0.0555001\pi\) |
0.173476 | + | 0.984838i | \(0.444500\pi\) | |||||||
\(308\) | −14.9238 | + | 3.99883i | −0.850365 | + | 0.227855i | ||||
\(309\) | 3.40192 | − | 10.7033i | 0.193528 | − | 0.608892i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.9868 | + | 6.92056i | −0.679707 | + | 0.392429i | −0.799745 | − | 0.600340i | \(-0.795032\pi\) |
0.120038 | + | 0.992769i | \(0.461698\pi\) | |||||||
\(312\) | 1.52294 | − | 0.788332i | 0.0862196 | − | 0.0446305i | ||||
\(313\) | 4.79847 | + | 17.9081i | 0.271226 | + | 1.01223i | 0.958329 | + | 0.285668i | \(0.0922154\pi\) |
−0.687103 | + | 0.726560i | \(0.741118\pi\) | |||||||
\(314\) | −9.12554 | −0.514984 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.5711 | 0.763431 | ||||||||
\(317\) | −0.217566 | − | 0.811966i | −0.0122197 | − | 0.0456046i | 0.959547 | − | 0.281549i | \(-0.0908483\pi\) |
−0.971766 | + | 0.235945i | \(0.924182\pi\) | |||||||
\(318\) | 7.56176 | + | 4.84194i | 0.424043 | + | 0.271522i | ||||
\(319\) | 14.8399 | − | 8.56781i | 0.830874 | − | 0.479705i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.10845 | + | 6.69716i | 0.340941 | + | 0.373799i | ||||
\(322\) | 19.7876 | − | 5.30208i | 1.10272 | − | 0.295473i | ||||
\(323\) | −0.226641 | − | 0.226641i | −0.0126107 | − | 0.0126107i | ||||
\(324\) | −8.48528 | + | 3.00000i | −0.471405 | + | 0.166667i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6.17086 | − | 3.56275i | −0.341772 | − | 0.197322i | ||||
\(327\) | 12.6334 | + | 0.580793i | 0.698629 | + | 0.0321179i | ||||
\(328\) | −7.98343 | − | 2.13915i | −0.440811 | − | 0.118115i | ||||
\(329\) | 6.73825 | + | 11.6710i | 0.371492 | + | 0.643443i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.08211 | − | 3.60631i | 0.114443 | − | 0.198221i | −0.803114 | − | 0.595825i | \(-0.796825\pi\) |
0.917557 | + | 0.397604i | \(0.130158\pi\) | |||||||
\(332\) | 4.94803 | − | 4.94803i | 0.271558 | − | 0.271558i | ||||
\(333\) | 8.86483 | + | 10.6642i | 0.485790 | + | 0.584397i | ||||
\(334\) | 10.8332i | 0.592766i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 6.41822 | + | 2.03995i | 0.350143 | + | 0.111288i | ||||
\(337\) | 0.840764 | − | 3.13777i | 0.0457993 | − | 0.170925i | −0.939238 | − | 0.343267i | \(-0.888467\pi\) |
0.985037 | + | 0.172341i | \(0.0551332\pi\) | |||||||
\(338\) | 3.11093 | − | 11.6102i | 0.169213 | − | 0.631510i | ||||
\(339\) | −6.96478 | − | 2.21367i | −0.378275 | − | 0.120230i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 37.3656i | 2.02346i | ||||||||
\(342\) | −5.57334 | + | 0.956233i | −0.301372 | + | 0.0517072i | ||||
\(343\) | −3.07470 | + | 3.07470i | −0.166018 | + | 0.166018i | ||||
\(344\) | −1.03157 | + | 1.78674i | −0.0556188 | + | 0.0963346i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.88492 | − | 3.26478i | −0.101334 | − | 0.175516i | ||||
\(347\) | −4.53334 | − | 1.21470i | −0.243362 | − | 0.0652087i | 0.135076 | − | 0.990835i | \(-0.456872\pi\) |
−0.378438 | + | 0.925627i | \(0.623539\pi\) | |||||||
\(348\) | −7.46134 | − | 0.343019i | −0.399970 | − | 0.0183877i | ||||
\(349\) | −8.42818 | − | 4.86601i | −0.451150 | − | 0.260472i | 0.257166 | − | 0.966367i | \(-0.417211\pi\) |
−0.708316 | + | 0.705896i | \(0.750545\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.00162 | − | 4.73929i | 0.106839 | − | 0.252965i | ||||
\(352\) | −2.80977 | − | 2.80977i | −0.149761 | − | 0.149761i | ||||
\(353\) | 4.92815 | − | 1.32049i | 0.262299 | − | 0.0702827i | −0.125273 | − | 0.992122i | \(-0.539981\pi\) |
0.387572 | + | 0.921840i | \(0.373314\pi\) | |||||||
\(354\) | 6.37008 | + | 6.98400i | 0.338566 | + | 0.371195i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.22474 | + | 2.43916i | −0.223911 | + | 0.129275i | ||||
\(357\) | 0.964409 | + | 0.617529i | 0.0510420 | + | 0.0326831i | ||||
\(358\) | −3.33754 | − | 12.4559i | −0.176394 | − | 0.658312i | ||||
\(359\) | −1.27697 | −0.0673957 | −0.0336978 | − | 0.999432i | \(-0.510728\pi\) | ||||
−0.0336978 | + | 0.999432i | \(0.510728\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.4471 | 0.813003 | ||||||||
\(362\) | 6.29441 | + | 23.4910i | 0.330827 | + | 1.23466i | ||||
\(363\) | 7.36727 | − | 3.81358i | 0.386682 | − | 0.200161i | ||||
\(364\) | −3.33392 | + | 1.92484i | −0.174745 | + | 0.100889i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4.57097 | + | 14.3815i | −0.238928 | + | 0.751731i | ||||
\(367\) | −9.74300 | + | 2.61063i | −0.508581 | + | 0.136274i | −0.503979 | − | 0.863716i | \(-0.668131\pi\) |
−0.00460117 | + | 0.999989i | \(0.501465\pi\) | |||||||
\(368\) | 3.72549 | + | 3.72549i | 0.194204 | + | 0.194204i | ||||
\(369\) | −22.5202 | + | 10.3751i | −1.17235 | + | 0.540105i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.4564 | − | 10.0785i | −0.906293 | − | 0.523249i | ||||
\(372\) | 8.78279 | − | 13.7163i | 0.455367 | − | 0.711156i | ||||
\(373\) | −12.6656 | − | 3.39374i | −0.655801 | − | 0.175721i | −0.0844507 | − | 0.996428i | \(-0.526914\pi\) |
−0.571350 | + | 0.820706i | \(0.693580\pi\) | |||||||
\(374\) | −0.337843 | − | 0.585162i | −0.0174695 | − | 0.0302580i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.73299 | + | 3.00162i | −0.0893720 | + | 0.154797i | ||||
\(377\) | 3.01907 | − | 3.01907i | 0.155490 | − | 0.155490i | ||||
\(378\) | 18.7190 | − | 7.60229i | 0.962800 | − | 0.391019i | ||||
\(379\) | 0.587648i | 0.0301854i | 0.999886 | + | 0.0150927i | \(0.00480434\pi\) | ||||
−0.999886 | + | 0.0150927i | \(0.995196\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −24.9515 | + | 22.7582i | −1.27830 | + | 1.16594i | ||||
\(382\) | −3.52759 | + | 13.1652i | −0.180487 | + | 0.673588i | ||||
\(383\) | −3.75319 | + | 14.0071i | −0.191779 | + | 0.715729i | 0.801298 | + | 0.598265i | \(0.204143\pi\) |
−0.993077 | + | 0.117464i | \(0.962524\pi\) | |||||||
\(384\) | 0.370982 | + | 1.69185i | 0.0189316 | + | 0.0863371i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 16.2043i | − | 0.824775i | ||||||
\(387\) | 1.04665 | + | 6.10031i | 0.0532041 | + | 0.310096i | ||||
\(388\) | 1.05794 | − | 1.05794i | 0.0537090 | − | 0.0537090i | ||||
\(389\) | 10.3789 | − | 17.9767i | 0.526230 | − | 0.911456i | −0.473303 | − | 0.880899i | \(-0.656939\pi\) |
0.999533 | − | 0.0305570i | \(-0.00972810\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.447948 | + | 0.775869i | 0.0226537 | + | 0.0392374i | ||||
\(392\) | −7.84169 | − | 2.10118i | −0.396065 | − | 0.106125i | ||||
\(393\) | 3.56957 | + | 6.89588i | 0.180061 | + | 0.347851i | ||||
\(394\) | −1.42175 | − | 0.820845i | −0.0716265 | − | 0.0413536i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −11.8705 | − | 1.09376i | −0.596517 | − | 0.0549633i | ||||
\(397\) | −15.7430 | − | 15.7430i | −0.790118 | − | 0.790118i | 0.191395 | − | 0.981513i | \(-0.438699\pi\) |
−0.981513 | + | 0.191395i | \(0.938699\pi\) | |||||||
\(398\) | 16.5881 | − | 4.44477i | 0.831487 | − | 0.222796i | ||||
\(399\) | 12.3996 | − | 2.71893i | 0.620758 | − | 0.136117i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.11737 | − | 2.37716i | 0.205612 | − | 0.118710i | −0.393659 | − | 0.919257i | \(-0.628791\pi\) |
0.599270 | + | 0.800547i | \(0.295457\pi\) | |||||||
\(402\) | 0.647729 | − | 14.0894i | 0.0323058 | − | 0.702715i | ||||
\(403\) | 2.40966 | + | 8.99298i | 0.120034 | + | 0.447972i | ||||
\(404\) | 10.2993 | 0.512408 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 16.7674 | 0.832153 | ||||||||
\(407\) | 4.75404 | + | 17.7423i | 0.235649 | + | 0.879454i | ||||
\(408\) | −0.0135258 | + | 0.294213i | −0.000669627 | + | 0.0145657i | ||||
\(409\) | 25.8797 | − | 14.9417i | 1.27967 | − | 0.738817i | 0.302882 | − | 0.953028i | \(-0.402051\pi\) |
0.976787 | + | 0.214211i | \(0.0687180\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 21.1461 | − | 4.63682i | 1.04306 | − | 0.228718i | ||||
\(412\) | −6.26326 | + | 1.67823i | −0.308568 | + | 0.0826807i | ||||
\(413\) | −15.0049 | − | 15.0049i | −0.738343 | − | 0.738343i | ||||
\(414\) | 15.7392 | + | 1.45022i | 0.773541 | + | 0.0712744i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.857441 | − | 0.495044i | −0.0420395 | − | 0.0242715i | ||||
\(417\) | −3.31384 | − | 6.40185i | −0.162280 | − | 0.313500i | ||||
\(418\) | −7.23474 | − | 1.93854i | −0.353863 | − | 0.0948172i | ||||
\(419\) | −8.81638 | − | 15.2704i | −0.430708 | − | 0.746009i | 0.566226 | − | 0.824250i | \(-0.308403\pi\) |
−0.996934 | + | 0.0782412i | \(0.975070\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.9462 | − | 24.1555i | 0.679696 | − | 1.17727i | −0.295377 | − | 0.955381i | \(-0.595445\pi\) |
0.975072 | − | 0.221887i | \(-0.0712215\pi\) | |||||||
\(422\) | 12.8820 | − | 12.8820i | 0.627085 | − | 0.627085i | ||||
\(423\) | 1.75831 | + | 10.2482i | 0.0854919 | + | 0.498284i | ||||
\(424\) | − | 5.18410i | − | 0.251762i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.57799 | + | 11.7569i | 0.124904 | + | 0.569623i | ||||
\(427\) | 8.76775 | − | 32.7217i | 0.424301 | − | 1.58351i | ||||
\(428\) | 1.35450 | − | 5.05507i | 0.0654723 | − | 0.244346i | ||||
\(429\) | 5.03461 | − | 4.59205i | 0.243073 | − | 0.221706i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.2910i | 0.929215i | 0.885517 | + | 0.464608i | \(0.153805\pi\) | ||||
−0.885517 | + | 0.464608i | \(0.846195\pi\) | |||||||
\(432\) | 4.10039 | + | 3.19168i | 0.197280 | + | 0.153560i | ||||
\(433\) | −16.7154 | + | 16.7154i | −0.803292 | + | 0.803292i | −0.983609 | − | 0.180316i | \(-0.942288\pi\) |
0.180316 | + | 0.983609i | \(0.442288\pi\) | |||||||
\(434\) | −18.2814 | + | 31.6642i | −0.877533 | + | 1.51993i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.65080 | − | 6.32337i | −0.174842 | − | 0.302835i | ||||
\(437\) | 9.59259 | + | 2.57033i | 0.458876 | + | 0.122955i | ||||
\(438\) | 10.9332 | − | 17.0747i | 0.522410 | − | 0.815860i | ||||
\(439\) | 31.1811 | + | 18.0024i | 1.48819 | + | 0.859209i | 0.999909 | − | 0.0134750i | \(-0.00428934\pi\) |
0.488285 | + | 0.872684i | \(0.337623\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −22.1203 | + | 10.1909i | −1.05335 | + | 0.485280i | ||||
\(442\) | −0.119047 | − | 0.119047i | −0.00566249 | − | 0.00566249i | ||||
\(443\) | 25.9195 | − | 6.94511i | 1.23147 | − | 0.329972i | 0.416320 | − | 0.909218i | \(-0.363320\pi\) |
0.815153 | + | 0.579246i | \(0.196653\pi\) | |||||||
\(444\) | 2.42521 | − | 7.63035i | 0.115095 | − | 0.362120i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.06659 | − | 2.34785i | 0.192559 | − | 0.111174i | ||||
\(447\) | 1.59431 | − | 0.825278i | 0.0754085 | − | 0.0390343i | ||||
\(448\) | −1.00635 | − | 3.75574i | −0.0475455 | − | 0.177442i | ||||
\(449\) | 41.3392 | 1.95092 | 0.975459 | − | 0.220182i | \(-0.0706652\pi\) | ||||
0.975459 | + | 0.220182i | \(0.0706652\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −32.8421 | −1.54647 | ||||||||
\(452\) | 1.09205 | + | 4.07557i | 0.0513655 | + | 0.191699i | ||||
\(453\) | 5.93526 | + | 3.80046i | 0.278863 | + | 0.178561i | ||||
\(454\) | 21.6778 | − | 12.5157i | 1.01739 | − | 0.587390i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.20010 | + | 2.41213i | 0.103029 | + | 0.112959i | ||||
\(457\) | 20.8557 | − | 5.58827i | 0.975589 | − | 0.261408i | 0.264403 | − | 0.964412i | \(-0.414825\pi\) |
0.711186 | + | 0.703004i | \(0.248158\pi\) | |||||||
\(458\) | −16.1135 | − | 16.1135i | −0.752935 | − | 0.752935i | ||||
\(459\) | 0.533019 | + | 0.704691i | 0.0248792 | + | 0.0328921i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.8706 | − | 6.27615i | −0.506295 | − | 0.292309i | 0.225015 | − | 0.974355i | \(-0.427757\pi\) |
−0.731309 | + | 0.682046i | \(0.761090\pi\) | |||||||
\(462\) | 26.7325 | + | 1.22897i | 1.24371 | + | 0.0571767i | ||||
\(463\) | 21.3514 | + | 5.72110i | 0.992286 | + | 0.265882i | 0.718210 | − | 0.695826i | \(-0.244962\pi\) |
0.274076 | + | 0.961708i | \(0.411628\pi\) | |||||||
\(464\) | 2.15618 | + | 3.73461i | 0.100098 | + | 0.173375i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.6011 | − | 25.2899i | 0.676383 | − | 1.17153i | ||||
\(467\) | 3.48137 | − | 3.48137i | 0.161099 | − | 0.161099i | −0.621955 | − | 0.783053i | \(-0.713661\pi\) |
0.783053 | + | 0.621955i | \(0.213661\pi\) | |||||||
\(468\) | −2.92749 | + | 0.502277i | −0.135323 | + | 0.0232178i | ||||
\(469\) | 31.6622i | 1.46203i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.0634 | + | 4.78769i | 0.694083 | + | 0.220605i | ||||
\(472\) | 1.41251 | − | 5.27158i | 0.0650163 | − | 0.242644i | ||||
\(473\) | −2.12184 | + | 7.91881i | −0.0975622 | + | 0.364107i | ||||
\(474\) | −22.4015 | − | 7.12002i | −1.02893 | − | 0.327033i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 0.661168i | − | 0.0303046i | ||||||
\(477\) | −9.94174 | − | 11.9598i | −0.455201 | − | 0.547599i | ||||
\(478\) | 6.45273 | − | 6.45273i | 0.295141 | − | 0.295141i | ||||
\(479\) | 1.35673 | − | 2.34993i | 0.0619906 | − | 0.107371i | −0.833364 | − | 0.552724i | \(-0.813588\pi\) |
0.895355 | + | 0.445353i | \(0.146922\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.28836 | + | 3.96356i | 0.104340 | + | 0.180723i | ||||
\(482\) | 1.68004 | + | 0.450166i | 0.0765239 | + | 0.0205045i | ||||
\(483\) | −35.4448 | − | 1.62949i | −1.61279 | − | 0.0741446i | ||||
\(484\) | −4.14790 | − | 2.39479i | −0.188541 | − | 0.108854i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 15.5804 | − | 0.500258i | 0.706743 | − | 0.0226921i | ||||
\(487\) | 8.20799 | + | 8.20799i | 0.371940 | + | 0.371940i | 0.868183 | − | 0.496244i | \(-0.165288\pi\) |
−0.496244 | + | 0.868183i | \(0.665288\pi\) | |||||||
\(488\) | 8.41558 | − | 2.25495i | 0.380955 | − | 0.102077i | ||||
\(489\) | 8.31692 | + | 9.11848i | 0.376104 | + | 0.412352i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.28058 | − | 2.47139i | 0.193180 | − | 0.111532i | −0.400290 | − | 0.916388i | \(-0.631091\pi\) |
0.593470 | + | 0.804856i | \(0.297757\pi\) | |||||||
\(492\) | 12.0558 | + | 7.71955i | 0.543517 | + | 0.348024i | ||||
\(493\) | 0.189789 | + | 0.708301i | 0.00854766 | + | 0.0319003i | ||||
\(494\) | −1.86624 | −0.0839661 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9.40344 | −0.422227 | ||||||||
\(497\) | −6.99322 | − | 26.0991i | −0.313689 | − | 1.17070i | ||||
\(498\) | −10.7636 | + | 5.57164i | −0.482328 | + | 0.249671i | ||||
\(499\) | −28.1148 | + | 16.2321i | −1.25859 | + | 0.726649i | −0.972801 | − | 0.231643i | \(-0.925590\pi\) |
−0.285791 | + | 0.958292i | \(0.592256\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.68361 | − | 17.8821i | 0.253925 | − | 0.798915i | ||||
\(502\) | −5.95736 | + | 1.59627i | −0.265890 | + | 0.0712450i | ||||
\(503\) | 19.6817 | + | 19.6817i | 0.877565 | + | 0.877565i | 0.993282 | − | 0.115717i | \(-0.0369166\pi\) |
−0.115717 | + | 0.993282i | \(0.536917\pi\) | |||||||
\(504\) | −9.52417 | − | 6.73461i | −0.424240 | − | 0.299983i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 18.1307 | + | 10.4677i | 0.806007 | + | 0.465348i | ||||
\(507\) | −11.2264 | + | 17.5325i | −0.498582 | + | 0.778647i | ||||
\(508\) | 18.8336 | + | 5.04645i | 0.835606 | + | 0.223900i | ||||
\(509\) | 5.25069 | + | 9.09446i | 0.232733 | + | 0.403105i | 0.958611 | − | 0.284718i | \(-0.0918999\pi\) |
−0.725879 | + | 0.687823i | \(0.758567\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22.7575 | + | 39.4171i | −1.00673 | + | 1.74371i | ||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 9.70148 | + | 1.34560i | 0.428331 | + | 0.0594098i | ||||
\(514\) | − | 29.0534i | − | 1.28149i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.64021 | − | 2.40812i | 0.116229 | − | 0.106012i | ||||
\(517\) | −3.56457 | + | 13.3031i | −0.156770 | + | 0.585072i | ||||
\(518\) | −4.65189 | + | 17.3611i | −0.204392 | + | 0.762802i | ||||
\(519\) | 1.39855 | + | 6.37804i | 0.0613893 | + | 0.279965i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 28.2545i | − | 1.23785i | −0.785450 | − | 0.618925i | \(-0.787568\pi\) | ||
0.785450 | − | 0.618925i | \(-0.212432\pi\) | |||||||
\(522\) | 12.1363 | + | 4.48079i | 0.531192 | + | 0.196119i | ||||
\(523\) | −13.6590 | + | 13.6590i | −0.597266 | + | 0.597266i | −0.939584 | − | 0.342318i | \(-0.888788\pi\) |
0.342318 | + | 0.939584i | \(0.388788\pi\) | |||||||
\(524\) | 2.24156 | − | 3.88249i | 0.0979230 | − | 0.169608i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.33036 | + | 16.1607i | 0.406823 | + | 0.704638i | ||||
\(527\) | −1.54451 | − | 0.413850i | −0.0672798 | − | 0.0180276i | ||||
\(528\) | 3.16389 | + | 6.11216i | 0.137691 | + | 0.265998i | ||||
\(529\) | −4.12099 | − | 2.37925i | −0.179173 | − | 0.103446i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.85082 | − | 14.8704i | −0.297300 | − | 0.645320i | ||||
\(532\) | −5.18240 | − | 5.18240i | −0.224685 | − | 0.224685i | ||||
\(533\) | −7.90429 | + | 2.11795i | −0.342373 | + | 0.0917385i | ||||
\(534\) | 8.25340 | − | 1.80977i | 0.357160 | − | 0.0783163i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7.05213 | + | 4.07155i | −0.304606 | + | 0.175864i | ||||
\(537\) | −1.02573 | + | 22.3117i | −0.0442635 | + | 0.962819i | ||||
\(538\) | −4.02601 | − | 15.0253i | −0.173574 | − | 0.647786i | ||||
\(539\) | −32.2590 | −1.38949 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.7216 | −1.14885 | −0.574427 | − | 0.818556i | \(-0.694775\pi\) | ||||
−0.574427 | + | 0.818556i | \(0.694775\pi\) | |||||||
\(542\) | −0.484468 | − | 1.80806i | −0.0208097 | − | 0.0776628i | ||||
\(543\) | 1.93447 | − | 42.0785i | 0.0830160 | − | 1.80576i | ||||
\(544\) | 0.147262 | − | 0.0850217i | 0.00631380 | − | 0.00364528i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 6.51311 | − | 1.42816i | 0.278735 | − | 0.0611197i | ||||
\(547\) | 0.234244 | − | 0.0627654i | 0.0100155 | − | 0.00268365i | −0.253808 | − | 0.967255i | \(-0.581683\pi\) |
0.263823 | + | 0.964571i | \(0.415016\pi\) | |||||||
\(548\) | −8.83798 | − | 8.83798i | −0.377540 | − | 0.377540i | ||||
\(549\) | 15.0904 | − | 21.3411i | 0.644043 | − | 0.910814i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.03946 | + | 4.06423i | 0.299891 | + | 0.173142i | ||||
\(552\) | −4.19502 | − | 8.10415i | −0.178552 | − | 0.344936i | ||||
\(553\) | 50.9693 | + | 13.6572i | 2.16744 | + | 0.580763i | ||||
\(554\) | −2.06556 | − | 3.57765i | −0.0877571 | − | 0.152000i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.08097 | + | 3.60435i | −0.0882528 | + | 0.152858i | ||||
\(557\) | 31.4838 | − | 31.4838i | 1.33401 | − | 1.33401i | 0.432266 | − | 0.901746i | \(-0.357714\pi\) |
0.901746 | − | 0.432266i | \(-0.142286\pi\) | |||||||
\(558\) | −21.6938 | + | 18.0333i | −0.918372 | + | 0.763412i | ||||
\(559\) | 2.04270i | 0.0863969i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.250667 | + | 1.14316i | 0.0105832 | + | 0.0482644i | ||||
\(562\) | −0.0743081 | + | 0.277322i | −0.00313450 | + | 0.0116981i | ||||
\(563\) | −8.35388 | + | 31.1771i | −0.352074 | + | 1.31396i | 0.532053 | + | 0.846711i | \(0.321421\pi\) |
−0.884127 | + | 0.467247i | \(0.845246\pi\) | |||||||
\(564\) | 4.43540 | − | 4.04551i | 0.186764 | − | 0.170347i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 18.1025i | − | 0.760904i | ||||||
\(567\) | −34.8876 | + | 2.72808i | −1.46514 | + | 0.114569i | ||||
\(568\) | 4.91376 | − | 4.91376i | 0.206177 | − | 0.206177i | ||||
\(569\) | 16.1545 | − | 27.9804i | 0.677232 | − | 1.17300i | −0.298580 | − | 0.954385i | \(-0.596513\pi\) |
0.975811 | − | 0.218615i | \(-0.0701538\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.9565 | + | 22.4413i | 0.542213 | + | 0.939141i | 0.998777 | + | 0.0494501i | \(0.0157469\pi\) |
−0.456563 | + | 0.889691i | \(0.650920\pi\) | |||||||
\(572\) | −3.80016 | − | 1.01825i | −0.158893 | − | 0.0425752i | ||||
\(573\) | 12.7300 | − | 19.8807i | 0.531803 | − | 0.830529i | ||||
\(574\) | −27.8310 | − | 16.0682i | −1.16164 | − | 0.670674i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.275255 | − | 2.98735i | 0.0114690 | − | 0.124473i | ||||
\(577\) | −6.10724 | − | 6.10724i | −0.254248 | − | 0.254248i | 0.568462 | − | 0.822710i | \(-0.307539\pi\) |
−0.822710 | + | 0.568462i | \(0.807539\pi\) | |||||||
\(578\) | −16.3928 | + | 4.39244i | −0.681851 | + | 0.182701i | ||||
\(579\) | −8.50152 | + | 26.7480i | −0.353311 | + | 1.11161i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 23.5629 | − | 13.6041i | 0.977556 | − | 0.564392i | ||||
\(582\) | −2.30138 | + | 1.19128i | −0.0953951 | + | 0.0493801i | ||||
\(583\) | −5.33157 | − | 19.8977i | −0.220811 | − | 0.824077i | ||||
\(584\) | −11.7058 | −0.484391 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −21.3953 | −0.883833 | ||||||||
\(587\) | −0.490414 | − | 1.83025i | −0.0202415 | − | 0.0755424i | 0.955066 | − | 0.296392i | \(-0.0957836\pi\) |
−0.975308 | + | 0.220850i | \(0.929117\pi\) | |||||||
\(588\) | 11.8418 | + | 7.58249i | 0.488346 | + | 0.312697i | ||||
\(589\) | −15.3501 | + | 8.86238i | −0.632490 | + | 0.365168i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.91619 | + | 2.10087i | 0.0788217 | + | 0.0864182i | ||||
\(592\) | −4.46504 | + | 1.19640i | −0.183512 | + | 0.0491719i | ||||
\(593\) | −11.0077 | − | 11.0077i | −0.452033 | − | 0.452033i | 0.443996 | − | 0.896029i | \(-0.353561\pi\) |
−0.896029 | + | 0.443996i | \(0.853561\pi\) | |||||||
\(594\) | 19.0206 | + | 8.03330i | 0.780426 | + | 0.329610i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.897625 | − | 0.518244i | −0.0367681 | − | 0.0212281i | ||||
\(597\) | −29.7136 | − | 1.36602i | −1.21610 | − | 0.0559074i | ||||
\(598\) | 5.03866 | + | 1.35011i | 0.206046 | + | 0.0552099i | ||||
\(599\) | 12.9428 | + | 22.4176i | 0.528828 | + | 0.915957i | 0.999435 | + | 0.0336142i | \(0.0107018\pi\) |
−0.470607 | + | 0.882343i | \(0.655965\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.79604 | + | 16.9672i | −0.399589 | + | 0.692108i | −0.993675 | − | 0.112293i | \(-0.964180\pi\) |
0.594086 | + | 0.804401i | \(0.297514\pi\) | |||||||
\(602\) | −5.67241 | + | 5.67241i | −0.231190 | + | 0.231190i | ||||
\(603\) | −8.46115 | + | 22.9172i | −0.344565 | + | 0.933262i | ||||
\(604\) | − | 4.06902i | − | 0.165566i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −17.0008 | − | 5.40349i | −0.690611 | − | 0.219502i | ||||
\(607\) | −7.70972 | + | 28.7731i | −0.312928 | + | 1.16786i | 0.612975 | + | 0.790102i | \(0.289973\pi\) |
−0.925903 | + | 0.377761i | \(0.876694\pi\) | |||||||
\(608\) | 0.487854 | − | 1.82070i | 0.0197851 | − | 0.0738390i | ||||
\(609\) | −27.6776 | − | 8.79699i | −1.12155 | − | 0.356472i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.43162i | 0.138828i | ||||||||
\(612\) | 0.176685 | − | 0.478556i | 0.00714207 | − | 0.0193445i | ||||
\(613\) | 12.5028 | − | 12.5028i | 0.504982 | − | 0.504982i | −0.408000 | − | 0.912982i | \(-0.633774\pi\) |
0.912982 | + | 0.408000i | \(0.133774\pi\) | |||||||
\(614\) | −14.3510 | + | 24.8566i | −0.579157 | + | 1.00313i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.72515 | − | 13.3804i | −0.311255 | − | 0.539110i | ||||
\(617\) | 7.14621 | + | 1.91482i | 0.287695 | + | 0.0770878i | 0.399781 | − | 0.916611i | \(-0.369086\pi\) |
−0.112085 | + | 0.993699i | \(0.535753\pi\) | |||||||
\(618\) | 11.2191 | + | 0.515774i | 0.451299 | + | 0.0207475i | ||||
\(619\) | −16.4624 | − | 9.50460i | −0.661682 | − | 0.382022i | 0.131236 | − | 0.991351i | \(-0.458105\pi\) |
−0.792917 | + | 0.609329i | \(0.791439\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −25.2196 | − | 10.6514i | −1.01203 | − | 0.427426i | ||||
\(622\) | −9.78715 | − | 9.78715i | −0.392429 | − | 0.392429i | ||||
\(623\) | −18.3217 | + | 4.90928i | −0.734043 | + | 0.196686i | ||||
\(624\) | 1.15564 | + | 1.26701i | 0.0462625 | + | 0.0507211i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −16.0560 | + | 9.26994i | −0.641727 | + | 0.370501i | ||||
\(627\) | 10.9252 | + | 6.99560i | 0.436310 | + | 0.279378i | ||||
\(628\) | −2.36186 | − | 8.81460i | −0.0942486 | − | 0.351741i | ||||
\(629\) | −0.786034 | −0.0313412 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.22853 | −0.0887165 | −0.0443583 | − | 0.999016i | \(-0.514124\pi\) | ||||
−0.0443583 | + | 0.999016i | \(0.514124\pi\) | |||||||
\(632\) | 3.51245 | + | 13.1086i | 0.139718 | + | 0.521433i | ||||
\(633\) | −28.0225 | + | 14.5055i | −1.11380 | + | 0.576543i | ||||
\(634\) | 0.727989 | − | 0.420305i | 0.0289121 | − | 0.0166924i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.71982 | + | 8.55729i | −0.107848 | + | 0.339319i | ||||
\(637\) | −7.76396 | + | 2.08035i | −0.307619 | + | 0.0824263i | ||||
\(638\) | 12.1167 | + | 12.1167i | 0.479705 | + | 0.479705i | ||||
\(639\) | 1.91278 | − | 20.7594i | 0.0756683 | − | 0.821229i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 37.8297 | + | 21.8410i | 1.49418 | + | 0.862666i | 0.999978 | − | 0.00667968i | \(-0.00212622\pi\) |
0.494204 | + | 0.869346i | \(0.335460\pi\) | |||||||
\(642\) | −4.88798 | + | 7.63367i | −0.192913 | + | 0.301277i | ||||
\(643\) | −29.4639 | − | 7.89483i | −1.16194 | − | 0.311342i | −0.374202 | − | 0.927347i | \(-0.622083\pi\) |
−0.787742 | + | 0.616006i | \(0.788750\pi\) | |||||||
\(644\) | 10.2428 | + | 17.7411i | 0.403624 | + | 0.699097i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.160260 | − | 0.277578i | 0.00630533 | − | 0.0109211i | ||||
\(647\) | −4.02651 | + | 4.02651i | −0.158298 | + | 0.158298i | −0.781812 | − | 0.623514i | \(-0.785704\pi\) |
0.623514 | + | 0.781812i | \(0.285704\pi\) | |||||||
\(648\) | −5.09393 | − | 7.41970i | −0.200108 | − | 0.291473i | ||||
\(649\) | − | 21.6861i | − | 0.851255i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 46.7892 | − | 42.6763i | 1.83381 | − | 1.67261i | ||||
\(652\) | 1.84421 | − | 6.88270i | 0.0722249 | − | 0.269547i | ||||
\(653\) | 8.44081 | − | 31.5015i | 0.330314 | − | 1.23275i | −0.578546 | − | 0.815650i | \(-0.696380\pi\) |
0.908861 | − | 0.417100i | \(-0.136954\pi\) | |||||||
\(654\) | 2.70876 | + | 12.3533i | 0.105921 | + | 0.483050i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 8.26506i | − | 0.322696i | ||||||
\(657\) | −27.0055 | + | 22.4487i | −1.05358 | + | 0.875809i | ||||
\(658\) | −9.52933 | + | 9.52933i | −0.371492 | + | 0.371492i | ||||
\(659\) | −7.75612 | + | 13.4340i | −0.302136 | + | 0.523314i | −0.976619 | − | 0.214975i | \(-0.931033\pi\) |
0.674484 | + | 0.738290i | \(0.264366\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.1307 | + | 19.2789i | 0.432933 | + | 0.749862i | 0.997124 | − | 0.0757821i | \(-0.0241453\pi\) |
−0.564191 | + | 0.825644i | \(0.690812\pi\) | |||||||
\(662\) | 4.02232 | + | 1.07778i | 0.156332 | + | 0.0418890i | ||||
\(663\) | 0.134051 | + | 0.258966i | 0.00520610 | + | 0.0100574i | ||||
\(664\) | 6.06007 | + | 3.49878i | 0.235176 | + | 0.135779i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.00649 | + | 11.3229i | −0.310245 | + | 0.438753i | ||||
\(667\) | −16.0656 | − | 16.0656i | −0.622063 | − | 0.622063i | ||||
\(668\) | −10.4641 | + | 2.80384i | −0.404867 | + | 0.108484i | ||||
\(669\) | −7.94444 | + | 1.74202i | −0.307150 | + | 0.0673503i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29.9817 | − | 17.3099i | 1.15743 | − | 0.668243i | ||||
\(672\) | −0.309282 | + | 6.72750i | −0.0119308 | + | 0.259519i | ||||
\(673\) | −2.49905 | − | 9.32657i | −0.0963312 | − | 0.359513i | 0.900887 | − | 0.434054i | \(-0.142917\pi\) |
−0.997218 | + | 0.0745413i | \(0.976251\pi\) | |||||||
\(674\) | 3.24846 | 0.125126 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.0197 | 0.462297 | ||||||||
\(677\) | −1.95869 | − | 7.30994i | −0.0752787 | − | 0.280944i | 0.918018 | − | 0.396539i | \(-0.129789\pi\) |
−0.993296 | + | 0.115596i | \(0.963122\pi\) | |||||||
\(678\) | 0.335620 | − | 7.30040i | 0.0128894 | − | 0.280370i | ||||
\(679\) | 5.03802 | − | 2.90870i | 0.193342 | − | 0.111626i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −42.3494 | + | 9.28618i | −1.62283 | + | 0.355847i | ||||
\(682\) | −36.0924 | + | 9.67093i | −1.38205 | + | 0.370319i | ||||
\(683\) | 7.48288 | + | 7.48288i | 0.286325 | + | 0.286325i | 0.835625 | − | 0.549300i | \(-0.185106\pi\) |
−0.549300 | + | 0.835625i | \(0.685106\pi\) | |||||||
\(684\) | −2.36614 | − | 5.13594i | −0.0904715 | − | 0.196378i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −3.76572 | − | 2.17414i | −0.143776 | − | 0.0830090i | ||||
\(687\) | 18.1443 | + | 35.0522i | 0.692250 | + | 1.33732i | ||||
\(688\) | −1.99285 | − | 0.533983i | −0.0759767 | − | 0.0203579i | ||||
\(689\) | −2.56635 | − | 4.44506i | −0.0977703 | − | 0.169343i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.3061 | − | 36.9033i | 0.810523 | − | 1.40387i | −0.101975 | − | 0.994787i | \(-0.532516\pi\) |
0.912498 | − | 0.409080i | \(-0.134150\pi\) | |||||||
\(692\) | 2.66569 | − | 2.66569i | 0.101334 | − | 0.101334i | ||||
\(693\) | −43.4820 | − | 16.0538i | −1.65174 | − | 0.609832i | ||||
\(694\) | − | 4.69326i | − | 0.178154i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.59981 | − | 7.29588i | −0.0606405 | − | 0.276550i | ||||
\(697\) | 0.363749 | − | 1.35753i | 0.0137780 | − | 0.0514201i | ||||
\(698\) | 2.51883 | − | 9.40041i | 0.0953392 | − | 0.355811i | ||||
\(699\) | −37.3700 | + | 34.0850i | −1.41346 | + | 1.28921i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 36.3602i | − | 1.37331i | −0.726985 | − | 0.686653i | \(-0.759079\pi\) | ||
0.726985 | − | 0.686653i | \(-0.240921\pi\) | |||||||
\(702\) | 5.09586 | + | 0.706799i | 0.192331 | + | 0.0266764i | ||||
\(703\) | −6.16113 | + | 6.16113i | −0.232371 | + | 0.232371i | ||||
\(704\) | 1.98681 | − | 3.44125i | 0.0748805 | − | 0.129697i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.55100 | + | 4.41846i | 0.0960080 | + | 0.166291i | ||||
\(707\) | 38.6814 | + | 10.3647i | 1.45476 | + | 0.389803i | ||||
\(708\) | −5.09733 | + | 7.96061i | −0.191569 | + | 0.299178i | ||||
\(709\) | 0.356646 | + | 0.205910i | 0.0133941 | + | 0.00773310i | 0.506682 | − | 0.862133i | \(-0.330872\pi\) |
−0.493288 | + | 0.869866i | \(0.664205\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 33.2421 | + | 23.5057i | 1.24668 | + | 0.881534i | ||||
\(712\) | −3.44949 | − | 3.44949i | −0.129275 | − | 0.129275i | ||||
\(713\) | 47.8551 | − | 12.8227i | 1.79219 | − | 0.480215i | ||||
\(714\) | −0.346880 | + | 1.09138i | −0.0129817 | + | 0.0408437i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11.1676 | − | 6.44762i | 0.417353 | − | 0.240959i | ||||
\(717\) | −14.0368 | + | 7.26599i | −0.524214 | + | 0.271353i | ||||
\(718\) | −0.330503 | − | 1.23345i | −0.0123343 | − | 0.0460321i | ||||
\(719\) | 34.4664 | 1.28538 | 0.642690 | − | 0.766126i | \(-0.277818\pi\) | ||||
0.642690 | + | 0.766126i | \(0.277818\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −25.2120 | −0.938946 | ||||||||
\(722\) | 3.99799 | + | 14.9207i | 0.148790 | + | 0.555291i | ||||
\(723\) | −2.53704 | − | 1.62451i | −0.0943534 | − | 0.0604162i | ||||
\(724\) | −21.0615 | + | 12.1599i | −0.782744 | + | 0.451918i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 5.59043 | + | 6.12921i | 0.207480 | + | 0.227476i | ||||
\(727\) | 13.7902 | − | 3.69508i | 0.511451 | − | 0.137043i | 0.00614188 | − | 0.999981i | \(-0.498045\pi\) |
0.505310 | + | 0.862938i | \(0.331378\pi\) | |||||||
\(728\) | −2.72214 | − | 2.72214i | −0.100889 | − | 0.100889i | ||||
\(729\) | −25.9808 | − | 7.34847i | −0.962250 | − | 0.272166i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.303823 | − | 0.175413i | −0.0112373 | − | 0.00648787i | ||||
\(732\) | −15.0745 | − | 0.693017i | −0.557169 | − | 0.0256146i | ||||
\(733\) | 29.6676 | + | 7.94942i | 1.09580 | + | 0.293618i | 0.761053 | − | 0.648690i | \(-0.224683\pi\) |
0.334746 | + | 0.942308i | \(0.391349\pi\) | |||||||
\(734\) | −5.04335 | − | 8.73534i | −0.186153 | − | 0.322427i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.63432 | + | 4.56277i | −0.0971022 | + | 0.168186i | ||||
\(737\) | −22.8802 | + | 22.8802i | −0.842803 | + | 0.842803i | ||||
\(738\) | −15.8502 | − | 19.0675i | −0.583454 | − | 0.701886i | ||||
\(739\) | − | 19.6312i | − | 0.722144i | −0.932538 | − | 0.361072i | \(-0.882411\pi\) | ||
0.932538 | − | 0.361072i | \(-0.117589\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.08056 | + | 0.979118i | 0.113167 | + | 0.0359688i | ||||
\(742\) | 5.21700 | − | 19.4701i | 0.191522 | − | 0.714771i | ||||
\(743\) | 9.31585 | − | 34.7672i | 0.341765 | − | 1.27549i | −0.554580 | − | 0.832130i | \(-0.687121\pi\) |
0.896346 | − | 0.443356i | \(-0.146212\pi\) | |||||||
\(744\) | 15.5221 | + | 4.93349i | 0.569067 | + | 0.180871i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 13.1124i | − | 0.480080i | ||||||
\(747\) | 20.6904 | − | 3.54991i | 0.757022 | − | 0.129884i | ||||
\(748\) | 0.477782 | − | 0.477782i | 0.0174695 | − | 0.0174695i | ||||
\(749\) | 10.1743 | − | 17.6224i | 0.371761 | − | 0.643910i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.4567 | − | 42.3603i | −0.892438 | − | 1.54575i | −0.836944 | − | 0.547289i | \(-0.815660\pi\) |
−0.0554938 | − | 0.998459i | \(-0.517673\pi\) | |||||||
\(752\) | −3.34787 | − | 0.897060i | −0.122084 | − | 0.0327124i | ||||
\(753\) | 10.6712 | + | 0.490584i | 0.388879 | + | 0.0178779i | ||||
\(754\) | 3.69759 | + | 2.13480i | 0.134658 | + | 0.0777449i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 12.1881 | + | 16.1135i | 0.443276 | + | 0.586043i | ||||
\(757\) | −22.9129 | − | 22.9129i | −0.832783 | − | 0.832783i | 0.155114 | − | 0.987897i | \(-0.450426\pi\) |
−0.987897 | + | 0.155114i | \(0.950426\pi\) | |||||||
\(758\) | −0.567624 | + | 0.152094i | −0.0206170 | + | 0.00552432i | ||||
\(759\) | −24.4361 | − | 26.7911i | −0.886973 | − | 0.972456i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.19124 | + | 5.30657i | −0.333182 | + | 0.192363i | −0.657253 | − | 0.753670i | \(-0.728282\pi\) |
0.324071 | + | 0.946033i | \(0.394948\pi\) | |||||||
\(762\) | −28.4406 | − | 18.2111i | −1.03030 | − | 0.659717i | ||||
\(763\) | −7.34795 | − | 27.4229i | −0.266014 | − | 0.992777i | ||||
\(764\) | −13.6296 | −0.493100 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −14.5012 | −0.523950 | ||||||||
\(767\) | −1.39851 | − | 5.21932i | −0.0504974 | − | 0.188459i | ||||
\(768\) | −1.53819 | + | 0.796225i | −0.0555046 | + | 0.0287313i | ||||
\(769\) | 3.31814 | − | 1.91573i | 0.119655 | − | 0.0690830i | −0.438978 | − | 0.898498i | \(-0.644659\pi\) |
0.558633 | + | 0.829415i | \(0.311326\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.2428 | + | 47.9578i | −0.548955 | + | 1.72716i | ||||
\(772\) | 15.6521 | − | 4.19397i | 0.563332 | − | 0.150944i | ||||
\(773\) | 19.8976 | + | 19.8976i | 0.715668 | + | 0.715668i | 0.967715 | − | 0.252047i | \(-0.0811037\pi\) |
−0.252047 | + | 0.967715i | \(0.581104\pi\) | |||||||
\(774\) | −5.62156 | + | 2.58986i | −0.202063 | + | 0.0930907i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.29571 | + | 0.748079i | 0.0465133 | + | 0.0268545i | ||||
\(777\) | 16.7872 | − | 26.2170i | 0.602239 | − | 0.940529i | ||||
\(778\) | 20.0504 | + | 5.37250i | 0.718843 | + | 0.192613i | ||||
\(779\) | −7.78950 | − | 13.4918i | −0.279088 | − | 0.483395i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.8065 | − | 23.9136i | 0.494036 | − | 0.855696i | ||||
\(782\) | −0.633495 | + | 0.633495i | −0.0226537 | + | 0.0226537i | ||||
\(783\) | −17.6823 | − | 13.7636i | −0.631915 | − | 0.491872i | ||||
\(784\) | − | 8.11832i | − | 0.289940i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −5.73704 | + | 5.23273i | −0.204633 | + | 0.186645i | ||||
\(787\) | 1.87155 | − | 6.98473i | 0.0667137 | − | 0.248979i | −0.924513 | − | 0.381150i | \(-0.875528\pi\) |
0.991227 | + | 0.132171i | \(0.0421948\pi\) | |||||||
\(788\) | 0.424901 | − | 1.58575i | 0.0151365 | − | 0.0564901i | ||||
\(789\) | −6.92279 | − | 31.5712i | −0.246458 | − | 1.12397i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.4058i | 0.583321i | ||||||||
\(792\) | −2.01584 | − | 11.7492i | −0.0716296 | − | 0.417488i | ||||
\(793\) | 6.09956 | − | 6.09956i | 0.216602 | − | 0.216602i | ||||
\(794\) | 11.1320 | − | 19.2811i | 0.395059 | − | 0.684262i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.58664 | + | 14.8725i | 0.304345 | + | 0.527142i | ||||
\(797\) | 33.4396 | + | 8.96012i | 1.18449 | + | 0.317384i | 0.796707 | − | 0.604366i | \(-0.206573\pi\) |
0.387786 | + | 0.921750i | \(0.373240\pi\) | |||||||
\(798\) | 5.83555 | + | 11.2734i | 0.206576 | + | 0.399074i | ||||
\(799\) | −0.510406 | − | 0.294683i | −0.0180569 | − | 0.0104251i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.5732 | − | 1.34278i | −0.514919 | − | 0.0474448i | ||||
\(802\) | 3.36182 | + | 3.36182i | 0.118710 | + | 0.118710i | ||||
\(803\) | −44.9295 | + | 12.0388i | −1.58553 | + | 0.424841i | ||||
\(804\) | 13.7769 | − | 3.02094i | 0.485875 | − | 0.106540i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.06289 | + | 4.65511i | −0.284003 | + | 0.163969i | ||||
\(807\) | −1.23732 | + | 26.9142i | −0.0435557 | + | 0.947424i | ||||
\(808\) | 2.66565 | + | 9.94834i | 0.0937772 | + | 0.349981i | ||||
\(809\) | −52.6028 | −1.84942 | −0.924709 | − | 0.380675i | \(-0.875692\pi\) | ||||
−0.924709 | + | 0.380675i | \(0.875692\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.8979 | −0.488021 | −0.244011 | − | 0.969773i | \(-0.578463\pi\) | ||||
−0.244011 | + | 0.969773i | \(0.578463\pi\) | |||||||
\(812\) | 4.33973 | + | 16.1961i | 0.152295 | + | 0.568371i | ||||
\(813\) | −0.148892 | + | 3.23870i | −0.00522188 | + | 0.113586i | ||||
\(814\) | −15.9073 | + | 9.18410i | −0.557551 | + | 0.321902i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.287689 | + | 0.0630830i | −0.0100711 | + | 0.00220835i | ||||
\(817\) | −3.75637 | + | 1.00652i | −0.131419 | + | 0.0352136i | ||||
\(818\) | 21.1307 | + | 21.1307i | 0.738817 | + | 0.738817i | ||||
\(819\) | −11.5003 | − | 1.05965i | −0.401854 | − | 0.0370270i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.9657 | − | 13.8366i | −0.836408 | − | 0.482900i | 0.0196338 | − | 0.999807i | \(-0.493750\pi\) |
−0.856042 | + | 0.516907i | \(0.827083\pi\) | |||||||
\(822\) | 9.95185 | + | 19.2255i | 0.347111 | + | 0.670566i | ||||
\(823\) | −29.1118 | − | 7.80049i | −1.01477 | − | 0.271908i | −0.287151 | − | 0.957885i | \(-0.592708\pi\) |
−0.727623 | + | 0.685977i | \(0.759375\pi\) | |||||||
\(824\) | −3.24210 | − | 5.61548i | −0.112944 | − | 0.195625i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.6101 | − | 18.3772i | 0.369172 | − | 0.639424i | ||||
\(827\) | 4.09863 | − | 4.09863i | 0.142523 | − | 0.142523i | −0.632245 | − | 0.774768i | \(-0.717866\pi\) |
0.774768 | + | 0.632245i | \(0.217866\pi\) | |||||||
\(828\) | 2.67281 | + | 15.5783i | 0.0928865 | + | 0.541382i | ||||
\(829\) | − | 37.6756i | − | 1.30853i | −0.756266 | − | 0.654264i | \(-0.772979\pi\) | ||
0.756266 | − | 0.654264i | \(-0.227021\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.53257 | + | 6.98924i | 0.0531642 | + | 0.242454i | ||||
\(832\) | 0.256253 | − | 0.956351i | 0.00888399 | − | 0.0331555i | ||||
\(833\) | 0.357291 | − | 1.33343i | 0.0123794 | − | 0.0462006i | ||||
\(834\) | 5.32603 | − | 4.85785i | 0.184425 | − | 0.168213i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 7.48995i | − | 0.259046i | ||||||
\(837\) | 45.2707 | − | 18.3857i | 1.56478 | − | 0.635501i | ||||
\(838\) | 12.4682 | − | 12.4682i | 0.430708 | − | 0.430708i | ||||
\(839\) | −16.5639 | + | 28.6895i | −0.571849 | + | 0.990471i | 0.424527 | + | 0.905415i | \(0.360440\pi\) |
−0.996376 | + | 0.0850559i | \(0.972893\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.20180 | + | 9.00978i | 0.179372 | + | 0.310682i | ||||
\(842\) | 26.9420 | + | 7.21908i | 0.928482 | + | 0.248786i | ||||
\(843\) | 0.268155 | − | 0.418784i | 0.00923575 | − | 0.0144237i | ||||
\(844\) | 15.7771 | + | 9.10894i | 0.543072 | + | 0.313543i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −9.44390 | + | 4.35082i | −0.324688 | + | 0.149584i | ||||
\(847\) | −13.1684 | − | 13.1684i | −0.452472 | − | 0.452472i | ||||
\(848\) | 5.00745 | − | 1.34174i | 0.171957 | − | 0.0460757i | ||||
\(849\) | −9.49743 | + | 29.8814i | −0.325951 | + | 1.02553i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 21.0916 | − | 12.1773i | 0.723011 | − | 0.417431i | ||||
\(852\) | −10.6890 | + | 5.53306i | −0.366201 | + | 0.189559i | ||||
\(853\) | −0.689663 | − | 2.57386i | −0.0236136 | − | 0.0881273i | 0.953113 | − | 0.302613i | \(-0.0978590\pi\) |
−0.976727 | + | 0.214486i | \(0.931192\pi\) | |||||||
\(854\) | 33.8760 | 1.15921 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.23339 | 0.178874 | ||||||||
\(857\) | −4.05364 | − | 15.1284i | −0.138470 | − | 0.516776i | −0.999959 | − | 0.00900123i | \(-0.997135\pi\) |
0.861490 | − | 0.507775i | \(-0.169532\pi\) | |||||||
\(858\) | 5.73863 | + | 3.67455i | 0.195914 | + | 0.125447i | ||||
\(859\) | −0.691191 | + | 0.399059i | −0.0235831 | + | 0.0136157i | −0.511745 | − | 0.859137i | \(-0.671001\pi\) |
0.488162 | + | 0.872753i | \(0.337667\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 37.5099 | + | 41.1249i | 1.27833 | + | 1.40153i | ||||
\(862\) | −18.6337 | + | 4.99288i | −0.634666 | + | 0.170058i | ||||
\(863\) | 30.2854 | + | 30.2854i | 1.03093 | + | 1.03093i | 0.999506 | + | 0.0314193i | \(0.0100027\pi\) |
0.0314193 | + | 0.999506i | \(0.489997\pi\) | |||||||
\(864\) | −2.02166 | + | 4.78674i | −0.0687783 | + | 0.162848i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −20.4721 | − | 11.8196i | −0.695671 | − | 0.401646i | ||||
\(867\) | 29.3638 | + | 1.34994i | 0.997246 | + | 0.0458462i | ||||
\(868\) | −35.3169 | − | 9.46313i | −1.19873 | − | 0.321199i | ||||
\(869\) | 26.9630 | + | 46.7013i | 0.914658 | + | 1.58423i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.03119 | + | 6.98222i | −0.136592 | + | 0.236584i | ||||
\(872\) | 5.16301 | − | 5.16301i | 0.174842 | − | 0.174842i | ||||
\(873\) | 4.42384 | − | 0.759010i | 0.149724 | − | 0.0256886i | ||||
\(874\) | 9.93098i | 0.335920i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 19.3226 | + | 6.14144i | 0.652850 | + | 0.207500i | ||||
\(877\) | −4.48641 | + | 16.7435i | −0.151495 | + | 0.565388i | 0.847885 | + | 0.530180i | \(0.177876\pi\) |
−0.999380 | + | 0.0352074i | \(0.988791\pi\) | |||||||
\(878\) | −9.31875 | + | 34.7780i | −0.314492 | + | 1.17370i | ||||
\(879\) | 35.3169 | + | 11.2250i | 1.19121 | + | 0.378610i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 15.1033i | − | 0.508843i | −0.967093 | − | 0.254421i | \(-0.918115\pi\) | ||
0.967093 | − | 0.254421i | \(-0.0818850\pi\) | |||||||
\(882\) | −15.5688 | − | 18.7290i | −0.524229 | − | 0.630639i | ||||
\(883\) | 16.4678 | − | 16.4678i | 0.554185 | − | 0.554185i | −0.373461 | − | 0.927646i | \(-0.621829\pi\) |
0.927646 | + | 0.373461i | \(0.121829\pi\) | |||||||
\(884\) | 0.0841789 | − | 0.145802i | 0.00283124 | − | 0.00490386i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.4169 | + | 23.2388i | 0.450750 | + | 0.780723i | ||||
\(887\) | −26.4123 | − | 7.07714i | −0.886837 | − | 0.237627i | −0.213482 | − | 0.976947i | \(-0.568481\pi\) |
−0.673355 | + | 0.739320i | \(0.735147\pi\) | |||||||
\(888\) | 7.99804 | + | 0.367692i | 0.268397 | + | 0.0123389i | ||||
\(889\) | 65.6556 | + | 37.9063i | 2.20202 | + | 1.27134i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −27.1823 | − | 23.2395i | −0.910643 | − | 0.778554i | ||||
\(892\) | 3.32036 | + | 3.32036i | 0.111174 | + | 0.111174i | ||||
\(893\) | −6.31049 | + | 1.69089i | −0.211173 | + | 0.0565835i | ||||
\(894\) | 1.20980 | + | 1.32639i | 0.0404616 | + | 0.0443612i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.36730 | − | 1.94411i | 0.112494 | − | 0.0649483i | ||||
\(897\) | −7.60889 | − | 4.87211i | −0.254053 | − | 0.162675i | ||||
\(898\) | 10.6994 | + | 39.9306i | 0.357043 | + | 1.33250i | ||||
\(899\) | 40.5510 | 1.35245 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.881522 | 0.0293678 | ||||||||
\(902\) | −8.50016 | − | 31.7230i | −0.283025 | − | 1.05626i | ||||
\(903\) | 12.3393 | − | 6.38732i | 0.410628 | − | 0.212557i | ||||
\(904\) | −3.65405 | + | 2.10967i | −0.121532 | + | 0.0701666i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.13480 | + | 6.71666i | −0.0709241 | + | 0.223146i | ||||
\(907\) | 24.7295 | − | 6.62626i | 0.821130 | − | 0.220021i | 0.176290 | − | 0.984338i | \(-0.443590\pi\) |
0.644841 | + | 0.764317i | \(0.276924\pi\) | |||||||
\(908\) | 17.6998 | + | 17.6998i | 0.587390 | + | 0.587390i | ||||
\(909\) | 25.2280 | + | 17.8389i | 0.836759 | + | 0.591678i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.55075 | + | 2.05003i | 0.117642 | + | 0.0679204i | 0.557666 | − | 0.830065i | \(-0.311697\pi\) |
−0.440025 | + | 0.897986i | \(0.645030\pi\) | |||||||
\(912\) | −1.76052 | + | 2.74944i | −0.0582965 | + | 0.0910430i | ||||
\(913\) | 26.8582 | + | 7.19662i | 0.888875 | + | 0.238173i | ||||
\(914\) | 10.7957 | + | 18.6987i | 0.357090 | + | 0.618499i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 11.3940 | − | 19.7350i | 0.376468 | − | 0.652061i | ||||
\(917\) | 12.3259 | − | 12.3259i | 0.407035 | − | 0.407035i | ||||
\(918\) | −0.542723 | + | 0.697245i | −0.0179125 | + | 0.0230125i | ||||
\(919\) | 28.8740i | 0.952464i | 0.879320 | + | 0.476232i | \(0.157998\pi\) | ||||
−0.879320 | + | 0.476232i | \(0.842002\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 36.7298 | − | 33.5011i | 1.21029 | − | 1.10390i | ||||
\(922\) | 3.24877 | − | 12.1246i | 0.106993 | − | 0.399302i | ||||
\(923\) | 1.78073 | − | 6.64579i | 0.0586135 | − | 0.218749i | ||||
\(924\) | 5.73178 | + | 26.1397i | 0.188562 | + | 0.859932i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 22.1046i | 0.726404i | ||||||||
\(927\) | −18.2486 | − | 6.73746i | −0.599362 | − | 0.221287i | ||||
\(928\) | −3.04930 | + | 3.04930i | −0.100098 | + | 0.100098i | ||||
\(929\) | 25.1077 | − | 43.4879i | 0.823758 | − | 1.42679i | −0.0791067 | − | 0.996866i | \(-0.525207\pi\) |
0.902865 | − | 0.429925i | \(-0.141460\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.65121 | − | 13.2523i | −0.250758 | − | 0.434326i | ||||
\(932\) | 28.2072 | + | 7.55809i | 0.923956 | + | 0.247573i | ||||
\(933\) | 11.0206 | + | 21.2903i | 0.360800 | + | 0.697012i | ||||
\(934\) | 4.26380 | + | 2.46170i | 0.139516 | + | 0.0805494i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.24285 | − | 2.69773i | −0.0406239 | − | 0.0881782i | ||||
\(937\) | 0.857094 | + | 0.857094i | 0.0280000 | + | 0.0280000i | 0.720968 | − | 0.692968i | \(-0.243697\pi\) |
−0.692968 | + | 0.720968i | \(0.743697\pi\) | |||||||
\(938\) | −30.5834 | + | 8.19479i | −0.998582 | + | 0.267569i | ||||
\(939\) | 31.3668 | − | 6.87796i | 1.02362 | − | 0.224454i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −43.4478 | + | 25.0846i | −1.41636 | + | 0.817735i | −0.995977 | − | 0.0896119i | \(-0.971437\pi\) |
−0.420382 | + | 0.907347i | \(0.638104\pi\) | |||||||
\(942\) | −0.725875 | + | 15.7892i | −0.0236503 | + | 0.514441i | ||||
\(943\) | 11.2704 | + | 42.0618i | 0.367015 | + | 1.36972i | ||||
\(944\) | 5.45754 | 0.177628 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.19815 | −0.266545 | ||||||||
\(947\) | −0.681485 | − | 2.54334i | −0.0221453 | − | 0.0826473i | 0.953969 | − | 0.299906i | \(-0.0969552\pi\) |
−0.976114 | + | 0.217258i | \(0.930289\pi\) | |||||||
\(948\) | 1.07949 | − | 23.4809i | 0.0350601 | − | 0.762626i | ||||
\(949\) | −10.0371 | + | 5.79490i | −0.325817 | + | 0.188111i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.42219 | + | 0.311851i | −0.0461176 | + | 0.0101125i | ||||
\(952\) | 0.638639 | − | 0.171123i | 0.0206984 | − | 0.00554612i | ||||
\(953\) | −28.1499 | − | 28.1499i | −0.911864 | − | 0.911864i | 0.0845545 | − | 0.996419i | \(-0.473053\pi\) |
−0.996419 | + | 0.0845545i | \(0.973053\pi\) | |||||||
\(954\) | 8.97912 | − | 12.6984i | 0.290710 | − | 0.411126i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 7.90295 | + | 4.56277i | 0.255600 | + | 0.147571i | ||||
\(957\) | −13.6438 | − | 26.3578i | −0.441042 | − | 0.852027i | ||||
\(958\) | 2.62100 | + | 0.702296i | 0.0846808 | + | 0.0226901i | ||||
\(959\) | −24.2991 | − | 42.0872i | −0.784658 | − | 1.35907i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.7123 | + | 49.7312i | −0.926204 | + | 1.60423i | ||||
\(962\) | −3.23623 | + | 3.23623i | −0.104340 | + | 0.104340i | ||||
\(963\) | 12.0735 | − | 10.0363i | 0.389062 | − | 0.323414i | ||||
\(964\) | 1.73931i | 0.0560194i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −7.59981 | − | 34.6587i | −0.244520 | − | 1.11513i | ||||
\(967\) | 0.343829 | − | 1.28319i | 0.0110568 | − | 0.0412646i | −0.960177 | − | 0.279392i | \(-0.909867\pi\) |
0.971234 | + | 0.238128i | \(0.0765337\pi\) | |||||||
\(968\) | 1.23963 | − | 4.62638i | 0.0398433 | − | 0.148697i | ||||
\(969\) | −0.410168 | + | 0.374112i | −0.0131765 | + | 0.0120182i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38.7906i | 1.24485i | 0.782679 | + | 0.622425i | \(0.213853\pi\) | ||||
−0.782679 | + | 0.622425i | \(0.786147\pi\) | |||||||
\(972\) | 4.51572 | + | 14.9201i | 0.144842 | + | 0.478561i | ||||
\(973\) | −11.4428 | + | 11.4428i | −0.366840 | + | 0.366840i | ||||
\(974\) | −5.80393 | + | 10.0527i | −0.185970 | + | 0.322109i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.35623 | + | 7.54520i | 0.139439 | + | 0.241516i | ||||
\(977\) | −41.4084 | − | 11.0953i | −1.32477 | − | 0.354972i | −0.474009 | − | 0.880520i | \(-0.657193\pi\) |
−0.850764 | + | 0.525548i | \(0.823860\pi\) | |||||||
\(978\) | −6.65520 | + | 10.3936i | −0.212810 | + | 0.332350i | ||||
\(979\) | −16.7875 | − | 9.69226i | −0.536530 | − | 0.309766i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.00980 | − | 21.8124i | 0.0641681 | − | 0.696417i | ||||
\(982\) | 3.49508 | + | 3.49508i | 0.111532 | + | 0.111532i | ||||
\(983\) | −31.1321 | + | 8.34182i | −0.992960 | + | 0.266063i | −0.718493 | − | 0.695534i | \(-0.755168\pi\) |
−0.274466 | + | 0.961597i | \(0.588501\pi\) | |||||||
\(984\) | −4.33624 | + | 13.6430i | −0.138234 | + | 0.434922i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.635046 | + | 0.366644i | −0.0202240 | + | 0.0116763i | ||||
\(987\) | 20.7294 | − | 10.7303i | 0.659824 | − | 0.341550i | ||||
\(988\) | −0.483018 | − | 1.80265i | −0.0153669 | − | 0.0573499i | ||||
\(989\) | 10.8700 | 0.345645 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.1017 | 0.638551 | 0.319275 | − | 0.947662i | \(-0.396561\pi\) | ||||
0.319275 | + | 0.947662i | \(0.396561\pi\) | |||||||
\(992\) | −2.43379 | − | 9.08302i | −0.0772729 | − | 0.288386i | ||||
\(993\) | −6.07411 | − | 3.88937i | −0.192756 | − | 0.123425i | ||||
\(994\) | 23.3998 | − | 13.5099i | 0.742196 | − | 0.428507i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −8.16761 | − | 8.95478i | −0.258801 | − | 0.283743i | ||||
\(997\) | 2.84912 | − | 0.763421i | 0.0902327 | − | 0.0241778i | −0.213420 | − | 0.976960i | \(-0.568460\pi\) |
0.303653 | + | 0.952783i | \(0.401794\pi\) | |||||||
\(998\) | −22.9557 | − | 22.9557i | −0.726649 | − | 0.726649i | ||||
\(999\) | 19.1567 | − | 14.4899i | 0.606090 | − | 0.458439i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 450.2.p.h.407.4 | 16 | ||
3.2 | odd | 2 | 1350.2.q.h.1007.1 | 16 | |||
5.2 | odd | 4 | 90.2.l.b.83.1 | yes | 16 | ||
5.3 | odd | 4 | inner | 450.2.p.h.443.4 | 16 | ||
5.4 | even | 2 | 90.2.l.b.47.1 | yes | 16 | ||
9.4 | even | 3 | 1350.2.q.h.557.2 | 16 | |||
9.5 | odd | 6 | inner | 450.2.p.h.257.4 | 16 | ||
15.2 | even | 4 | 270.2.m.b.143.4 | 16 | |||
15.8 | even | 4 | 1350.2.q.h.143.2 | 16 | |||
15.14 | odd | 2 | 270.2.m.b.197.3 | 16 | |||
20.7 | even | 4 | 720.2.cu.b.353.4 | 16 | |||
20.19 | odd | 2 | 720.2.cu.b.497.3 | 16 | |||
45.2 | even | 12 | 810.2.f.c.323.1 | 16 | |||
45.4 | even | 6 | 270.2.m.b.17.4 | 16 | |||
45.7 | odd | 12 | 810.2.f.c.323.8 | 16 | |||
45.13 | odd | 12 | 1350.2.q.h.1043.1 | 16 | |||
45.14 | odd | 6 | 90.2.l.b.77.1 | yes | 16 | ||
45.22 | odd | 12 | 270.2.m.b.233.3 | 16 | |||
45.23 | even | 12 | inner | 450.2.p.h.293.4 | 16 | ||
45.29 | odd | 6 | 810.2.f.c.647.8 | 16 | |||
45.32 | even | 12 | 90.2.l.b.23.1 | ✓ | 16 | ||
45.34 | even | 6 | 810.2.f.c.647.1 | 16 | |||
180.59 | even | 6 | 720.2.cu.b.257.4 | 16 | |||
180.167 | odd | 12 | 720.2.cu.b.113.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
90.2.l.b.23.1 | ✓ | 16 | 45.32 | even | 12 | ||
90.2.l.b.47.1 | yes | 16 | 5.4 | even | 2 | ||
90.2.l.b.77.1 | yes | 16 | 45.14 | odd | 6 | ||
90.2.l.b.83.1 | yes | 16 | 5.2 | odd | 4 | ||
270.2.m.b.17.4 | 16 | 45.4 | even | 6 | |||
270.2.m.b.143.4 | 16 | 15.2 | even | 4 | |||
270.2.m.b.197.3 | 16 | 15.14 | odd | 2 | |||
270.2.m.b.233.3 | 16 | 45.22 | odd | 12 | |||
450.2.p.h.257.4 | 16 | 9.5 | odd | 6 | inner | ||
450.2.p.h.293.4 | 16 | 45.23 | even | 12 | inner | ||
450.2.p.h.407.4 | 16 | 1.1 | even | 1 | trivial | ||
450.2.p.h.443.4 | 16 | 5.3 | odd | 4 | inner | ||
720.2.cu.b.113.3 | 16 | 180.167 | odd | 12 | |||
720.2.cu.b.257.4 | 16 | 180.59 | even | 6 | |||
720.2.cu.b.353.4 | 16 | 20.7 | even | 4 | |||
720.2.cu.b.497.3 | 16 | 20.19 | odd | 2 | |||
810.2.f.c.323.1 | 16 | 45.2 | even | 12 | |||
810.2.f.c.323.8 | 16 | 45.7 | odd | 12 | |||
810.2.f.c.647.1 | 16 | 45.34 | even | 6 | |||
810.2.f.c.647.8 | 16 | 45.29 | odd | 6 | |||
1350.2.q.h.143.2 | 16 | 15.8 | even | 4 | |||
1350.2.q.h.557.2 | 16 | 9.4 | even | 3 | |||
1350.2.q.h.1007.1 | 16 | 3.2 | odd | 2 | |||
1350.2.q.h.1043.1 | 16 | 45.13 | odd | 12 |